Sign chart (+ − +) for expanding a 3 × 3 determinant3 × 3 सारणिक के प्रसरण की चिह्न सारणी (+ − +)3 × 3 determinant expand karne ka sign chart (+ − +)

NCERT 4.2.3 · Class 12 Maths · Chapter 4 · interactive diagram

Parts and what they mean

• Plus (+) place (धन (+) स्थान) — Here i + j is even, e.g. (1,1), (1,3), (2,2): the cofactor equals the minor.
• Minus (−) place (ऋण (−) स्थान) — Here i + j is odd, e.g. (1,2), (2,1): the cofactor is minus the minor.
• Sign rule (-1)^{i+j} (चिह्न नियम (-1)^{i+j}) — i = row number, j = column number of the element.
• Rows R₁, R₂, R₃ (पंक्तियाँ R₁, R₂, R₃) — Horizontal lines of the determinant; i counts them from the top.
• Columns C₁, C₂, C₃ (स्तंभ C₁, C₂, C₃) — Vertical lines; j counts them from the left.
• Expanding along R₁ (R₁ के अनुदिश प्रसरण) — Use the signs of the first row: + − +.
• Chess-board pattern (शतरंज पैटर्न) — Signs alternate along every row and column, starting with + at the top-left.
• Expansion formula (प्रसरण सूत्र) — |A| = a_{11}M_{11} - a_{12}M_{12} + a_{13}M_{13}, where each M is a 2 × 2 minor.
• Same value every way (हर तरीके से एक ही मान) — All six expansions (R₁, R₂, R₃, C₁, C₂, C₃) give the same number.

Original diagram drawn by Simple Learning Hub, based on NCERT 4.2.3. Report a mistake